OFFSET
2,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 2..1000
FORMULA
a(n) < 2n^(3/2) - 1. Conjecturally a(n) << log^2 n. - Charles R Greathouse IV, Jun 03 2013
EXAMPLE
a(5) = 4 because largest square less than 5^3 is 121 and 125 - 121 = 4.
MATHEMATICA
lst = {}; Do[k = n^3; a = NextPrime[k, -1]; b = Floor@Sqrt[k - 1]^2; AppendTo[lst, k - Max[a, b]], {n, 2, 82}]; lst (* Arkadiusz Wesolowski, Jun 03 2013 *)
PROG
(Magma) [n^3-Maximum(Isqrt(n^3-1)^2, PreviousPrime(n^3)): n in [2..100]]; // Bruno Berselli, Jun 03 2013
(PARI) a(n)=n^3-max(sqrtint(n^3-1)^2, precprime(n^3)) \\ Charles R Greathouse IV, Jun 03 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Giovanni Teofilatto, Mar 08 2005
EXTENSIONS
Offset corrected by Michel Marcus, Jun 03 2013
Edited, corrected and extended by Arkadiusz Wesolowski, Jun 03 2013
STATUS
approved